By default, once the widget is on your home page, it will show the public timeline. If you want to use it to view your own or your friends timeline, you'll need to go to the prefs and enter your Twitter username (or email) and password. You can also elect to show the 'What are you doing' update section.
A more secure Google Gadget alternative exists where you do not need to provide your login details to a 3rd party.
Add GoogleGadget as friend to receive updates, or see the timeline: http://twitter.com/GoogleGadget
Please add any items you'd like to see that aren't already on the above To-do list.
Due to the lack of Google support for basic-auth passthrough and Twitter's inability to do any other sort of authorisation, any queries will pass through my server (twitter.isite.net.au). However I DO NOT store your username and password anywhere. ANYWHERE. It's not in the logs and it's not in any database. At some point I may log your username (and ONLY your username) for statistical analysis. This privacy notice will change to reflect that.
A more secure Google Gadget alternative exists where you do not need to provide your login details to a 3rd party.